The President-elect is likely “eligible” and can still take the oath.

The U.S. Supreme Court denied a petition to hear a claim that Barack Obama might, in effect, be ‘part Brit’, had dual nationality at birth, and is therefore not exclusively a “natural born” U.S. citizen “eligible to the office of President” under Article II, Section I of the Constitution. See AP, and SCOTUS and WSJ blogs. A stay application was filed in Donofrio v. Wells, Secretary of State of New Jersey (08A407). The Court sought no response to the petition, and gave no reasons for denial.